RosettaCodeData/Task/Legendre-prime-counting-fun.../Haskell/legendre-prime-counting-fun...

63 lines
2.5 KiB
Haskell

cTinyPhiPrimes :: [Int]
cTinyPhiPrimes = [ 2, 3, 5, 7, 11, 13 ]
cC :: Int
cC = length cTinyPhiPrimes - 1
cTinyPhiOddCirc :: Int
cTinyPhiOddCirc = product cTinyPhiPrimes `div` 2
cTinyPhiTot :: Int
cTinyPhiTot = product [ p - 1 | p <- cTinyPhiPrimes ]
cTinyPhiLUT :: UArray Int Word32
cTinyPhiLUT = runSTUArray $ do
ma <- newArray (0, cTinyPhiOddCirc - 1) 1
forM_ (drop 1 cTinyPhiPrimes) $ \ bp -> do
let i = (bp - 1) `shiftR` 1
let sqri = (i + i) * (i + 1)
unsafeWrite ma i 0
forM_ [ sqri, sqri + bp .. cTinyPhiOddCirc - 1 ] $ \ c -> unsafeWrite ma c 0
let tot i acc =
if i >= cTinyPhiOddCirc then return ma else do
v <- unsafeRead ma i
if v == 0 then do unsafeWrite ma i acc; tot (i + 1) acc
else do let nacc = acc + 1
unsafeWrite ma i nacc; tot (i + 1) nacc
tot 0 0
tinyPhi :: Word64 -> Int64
tinyPhi n =
let on = (n - 1) `shiftR` 1
numcyc = on `div` fromIntegral cTinyPhiOddCirc
rem = fromIntegral $ on - numcyc * fromIntegral cTinyPhiOddCirc
in fromIntegral numcyc * fromIntegral cTinyPhiTot +
fromIntegral (unsafeAt cTinyPhiLUT rem)
countPrimes :: Word64 -> Int64
countPrimes n =
if n < 3 then (if n < 2 then 0 else 1) else
let sqrtn = truncate $ sqrt $ fromIntegral n
qdrtn = truncate $ sqrt $ fromIntegral sqrtn
rtlmt = (sqrtn - 3) `div` 2
qrtlmt = (qdrtn - 3) `div` 2
oddPrimes@(UArray _ _ psz _) = runST $ do -- UArray of odd primes...
cmpsts <- newArray (0, rtlmt) False :: ST s (STUArray s Int Bool)
forM_ [ 0 .. qrtlmt ] $ \ i -> do
t <- unsafeRead cmpsts i
unless t $ do
let sqri = (i + i) * (i + 3) + 3
bp = i + i + 3
forM_ [ sqri, sqri + bp .. rtlmt ] $ \ c ->
unsafeWrite cmpsts c True
fcmpsts <- unsafeFreezeSTUArray cmpsts
let !numoprms = sum $ [ 1 | False <- elems fcmpsts ]
prms = [ fromIntegral $ i + i + 3 | (i, False) <- assocs fcmpsts ]
return $ listArray (0, numoprms - 1) prms :: ST s (UArray Int Word32)
lvl pi pilmt !m !acc =
if pi >= pilmt then acc else
let p = fromIntegral $ unsafeAt oddPrimes pi
nm = m * p in
if n <= nm * p then acc + fromIntegral (pilmt - pi) else
let !q = fromIntegral $ n `div` nm
!nacc = acc + tinyPhi q
!sacc = if pi <= cC then 0 else lvl cC pi nm 0
in lvl (pi + 1) pilmt m $ nacc - sacc
in tinyPhi n - lvl cC psz 1 0 + fromIntegral psz